Broody hens are hens who have entered a part of life when their hormones tell them to raise chicks. They walk around all puffed up, clucking loudly. They eventually settle into a nesting box and fluff out their feathers, often screaming and growling at anyone who comes close. Most broodies come out once a day to eat, drink, and poop, but sometimes a particularly dedicated broody will stay in the box - she needs to be removed daily to eat, or place food and water in front of her and take her out once a day to poop. Keep the nest clean. Some hens go broody multiple times a year, some will never go broody. This is driven by hormones and genetics.
If you have a broody hen, you can put eggs under her and she will hatch and care for the chicks. Occasionally one will not be a great mom, so make sure you have brooder supplies available just in case. Often a broody hen will be willing to adopt day old chicks - make sure the hen has been broody for at least two weeks if possible, and only introduce the chicks in the evening after the sun goes down. She will get familiar with their noises overnight, which will help introductions to go more smoothly in the morning.
If you decide to let her hatch eggs, leave the hen alone on hatching day. You can stop taking her out of her cage at day 19. Just clean up behind her daily. If you decide to give your broody some new babies, make sure they are under 5 days old or they often will not bond. Make sure your hen has been broody for over a week (I like to wait 2-3 weeks). Add babies at night so they can bond in the dark. Otherwise the hen could attack them.
Hens usually wean babies in between 4-10 weeks. Most of ours wean at 4-5 weeks, but some keep their babies for 2-4 months. Keep in mind - hen raised babies will NOT be as friendly as hand raised babies - but they are a lot less work since mama takes care of them!